A DISCRETE LIMIT THEOREM FOR L-FUNCTIONS OF ELLIPTIC CURVES

In the paper, we prove the discrete limit theorem in the sense of the weak convergence of probability measures in the space of analytic on DV = {s ∈ C : 1 < σ < 3/2, |t| < V} functions for L-functions of elliptic curves LE(s). The main statement of the paper is as follows. Let h > 0 be a fixed real number such that exp {2πk/h} is an irrational number for all k∈Z\{0}. Then the probability measure μN(LE(s + imh)∈A), A ∈ B(H(DV)), converges weakly to the measure PLE as N→∞.